When I turn the fuel cock on fuel starts to come out of the overflow and bubbles up through the main jet. The fuel cock is new (Yamaha OEM) and the needle and seat look good, The float  appears be adjusted properly.

I thought that fuel entered the float chamber through the needle and seat valve. I removed the float and attached a fuel line. When I turn on the fuel it pours in through the hole where the blue arrow is. Is this supposed to happen?
 

Definitely Not. That leads to a breather higher up. Better show what the fuel line is onto. Very odd situation.
Fuel feed in is that fitting sitting straight up in the carb pic. Expanding the pic i see something fitted to what i think is the breather mentioned. Is that the oil line clamped off.

Morley is correct the fuel line is the vertical fitting 

I'm sure ya under control but just wonder if ya going to run it without the oil pump. No problemo on premix but just a bit worried about the pump drive running dry in that bush. Maybe i saw your oil pump story yesterday on another post so don't worry--well me that's worrying lol.

Thanks everyone, yes I'm embarrassed to say that I had the fuel line hooked up to the vent. The oil line to the injection pump is clamped off as I am waiting for a oil pump seal. I ran it very briefly after I switched the line and checked the plug (had premix in the tank), running rich, plug is wet. I'll wait till I install the oil pump and see how things run. I realize that it will have know affect on the engine running rich.

Could just fit a bit of garden hose full of oil & blanked off in the end over the shaft & go play haha. I know i couldn't stop myself.